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<p>The initial value problem (IVP) solutions of two (3+2)-dimensional integrable nonlinear equations, such as generalized Sawada-Kotera (SK) and generalized Date-Jimbo-Kashiwara-Miwa (DJKM) equations, which are constructed by the extension of the corresponding two-dimensional equations, are solved by means of the non-local <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="42967_2025_520_Article_IEq1.gif" Format="GIF" Height="17" Rendition="HTML" Resolution="72" Type="Linedraw" Width="14" /> </InlineMediaObject> <EquationSource Format="TEX">\({\bar{\partial }}\)</EquationSource> <EquationSource Format="MATHML"><math> <mover accent="true"> <mrow> <mi>∂</mi> </mrow> <mrow> <mo stretchy="false">¯</mo> </mrow> </mover> </math></EquationSource> </InlineEquation>-method. The above significant results provide a good inspiration for dealing with similar high-dimensional nonlinear equations.</p>

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Solutions of Initial Value Problems of Two (3+2)-Dimensional Integrable Nonlinear Equations via Non-local \({\bar{\partial }}\)-Method

  • 期刊论文

  • 发表日期：

    2025年9月24日

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  • Linlin Gui,
  • Yufeng Zhang,
  • Siqi Han

摘要

The initial value problem (IVP) solutions of two (3+2)-dimensional integrable nonlinear equations, such as generalized Sawada-Kotera (SK) and generalized Date-Jimbo-Kashiwara-Miwa (DJKM) equations, which are constructed by the extension of the corresponding two-dimensional equations, are solved by means of the non-local \({\bar{\partial }}\) ∂ ¯ -method. The above significant results provide a good inspiration for dealing with similar high-dimensional nonlinear equations.